Lie symmetries, group-invariant solutions and conservation laws of the Vasicek pricing equation of mathematical finance

Chaudry Masood Khalique and Tanki Motsepa

Physica A: Statistical Mechanics and its Applications, 2018, vol. 505, issue C, 871-879

Abstract: The one-factor term structure model by Vasicek is analysed from the point of view of Lie symmetry analysis. Its one-parameter Lie point symmetries and corresponding group of adjoint representations are obtained. An optimal system of one-dimensional subalgebras is derived and is then used to obtain symmetry reductions and group-invariant solutions. The group-invariant solutions presented here are new and have not appeared in the literature. Moreover, we derive conservation laws for the Vasicek equation by employing the theorem due to Ibragimov.

Keywords: Vasicek pricing equation; Lie symmetry analysis; Optimal system of one-dimensional subalgebras; Group-invariant solutions; Conservation laws (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:505:y:2018:i:c:p:871-879

DOI: 10.1016/j.physa.2018.03.053

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